A056116 a(n) = 121*12^(n-2), a(0)=1, a(1)=10.

1, 10, 121, 1452, 17424, 209088, 2509056, 30108672, 361304064, 4335648768, 52027785216, 624333422592, 7492001071104, 89904012853248, 1078848154238976, 12946177850867712, 155354134210412544

Offset: 0

Author

Barry E. Williams, Jul 04 2000

Keywords

• nonn
• easy

Comments

For n >= 2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7,8,9,10,11,12} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4,5,6,7,8,9,10,11,12} we have f(x_1)<>y_1 and f(x_2)<> y_2. - Milan Janjic, Apr 19 2007

a(n) is the number of generalized compositions of n when there are 11*i-1 different types of i, (i=1,2,...). - Milan Janjic, Aug 26 2010

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Index entries for linear recurrences with constant coefficients, signature (12).

Crossrefs

Cf. A055996, A056002.

Programs

GAP

concatenation([1,10], List([2..20], n-> 121*12^(n-2) )); # G. C. Greubel, Jan 18 2020

Magma

[1,10] cat [121*12^(n-2): n in [2..20]]; // G. C. Greubel, Jan 18 2020

Maple

1,10, seq( 121*12^(n-2), n=2..20); # G. C. Greubel, Jan 18 2020

Mathematica

LinearRecurrence[{12},{1,10,121},20] (* Harvey P. Dale, Oct 20 2015 *)

PARI

concat([1, 10], vector(20, n, 121*12^(n-1) )) \\ G. C. Greubel, Jan 18 2020

Sage

[1,10]+[121*12^(n-2) for n in (2..20)] # G. C. Greubel, Jan 18 2020

Formula

a(n) = 12*a(n-1) + (-1)^n*C(2, 2-n).

G.f.: (1-x)^2/(1-12*x).

a(n) = Sum_{k=0..n} A201780(n,k)*10^k. - Philippe Deléham, Dec 05 2011

E.g.f.: (23 - 12*x + 121*exp(12*x))/144. - G. C. Greubel, Jan 18 2020

Extensions

More terms from James Sellers, Jul 04 2000